Reigning Masters champion Jordan Spieth, Jason Bohn and Brandt Snedeker finished one stroke behind Kirk after as they hit a 65, 63 and 67 respectively.
Kirk began his round with an impressive eagle at the par-five first and followed that up with five consecutive pars.
The 30-year-old suffered a slight setback when he registered a bogey on the seventh, but quickly made up for it with a birdie on the ninth.
Birdies at the 12th and 15th ensured Kirk stayed on track for the victory, but a hiccup at the last threatened to derail his charge.
A hooked tee shot put Kirk into a spot of bother and the 30-year-old compounded his problems when he fired his approach 155 yards past the green. However, he was able to salvage matters with a neat chip shot before sinking a seven-foot par putt to ensure that a playoff would not be required to determine the victor.
Spieth got off to a strong start, making birdies on the first and second, and he followed them up with a birdie on the fifth courtesy of a 27-foot putt, and a further birdie on the par-four sixth after sinking a 23-foot putt.
Spieth continued to excel during the first half of the back nine and recorded his fifth birdie of the round on the 13th. However, he slipped up on the 16th when he failed to make a seven-foot par putt and subsequently finished with a bogey.
He would make made amends for the error with his sixth birdie of the round on the 18th, but it would prove to be not quite enough to match Kirk.
Meanwhile, Bohn was absolutely unstoppable on the front nine as he produced six birdies in a row from the second to the seventh.
The birdie at the par-four fourth was particularly impressive, with the American sinking a 36-foot putt
Bohn's red-hot form carried on into the back nine as he made his seventh birdie of the round on the 12th. Despite carding a bogey on the 15th, he finished on a high as he recorded yet another birdie on the 16th.
Unlike Spieth and Bohn, Snedeker had a very turbulent final round, which began with consecutive birdies on the first and second.
He then carded a bogey on the fourth after missing an eight-foot putt for par, before bouncing back by sinking a 35-foot putt at the sixth and gaining a further shot at the seventh. But, he undid all his hard work once again by failing to convert a 10-foot par putt on the eighth, which resulted in him recording a bogey.
The same pattern occurred during the back nine as he made successive birdies on the 10th and 11th before registering his third bogey of the round on the 13th.
Sitting two strokes behind Kirk on the leaderboard were Pat Perez, Adam Hadwin, Kevin Kisner George McNeill and Ian Poulter.
Overnight leader Kevin Na finished tied 10th following his final round 72, which included three birdies, three bogeys and a double bogey on the par-four ninth.
Defending champion Adam Scott ended his tournament in tie for 24th after hitting a 70, which consisted of three birdies and three bogeys.